The present invention relates to a method for controlling a control arrangement controlling a predetermined system, the control arrangement comprising a controller, M output sensors providing an output signal vector y(t), L control actuators controlled by a control signal vector u(t) provided by the controller and N reference signal generators for providing a reference signal vector z(t) to the controller, L, M, N being positive integers, the output signal vector y(t) being defined as:
y(t)=d(t)+H(qxe2x88x921)u(t)
with:
d(t)=a disturbance signal vector of dimension Mxc3x971;
H(qxe2x88x921)=a transfer matrix of the predetermined system of dimension Mxc3x97L in a backward shift operator qxe2x88x921;
the control signal vector u(t) being defined as:
u(t)="PHgr"T(t)xc2x7w(t)
with:
"PHgr"T(t)=a block diagonal matrix of dimension Lxc3x97LNI built up of L row vectors
xcfx86T, each vector xcfx86T being the transpose of NIxc3x971 vector p containing the last I
samples of the N reference signals zn(t), I being an integer,
w(t)=a vector containing all controller coefficients for the controller.
Active control systems are generally formed by a number of actuators and sensors. The actuator outputs are controlled by actuator signals from a controller, based on inputs from both sensor signals and reference signals. Generally, the actuator signals are controlled such that desired sensor signals are obtained.
In e.g. active sound suppression systems the signal detected by the sensors should be minimal, which is obtained by adapting the actuator signals dependent on the reference signals and sensor signals. However, to obtain such a result, it might be necessary to control the actuators with high amplitude signals.
Certain actuators are limited with respect to the amplitude (or energy) with which they are controlled, and controlling the actuators with too high a signal might lead to non-linear behaviour (which is undesirable) or might even damage actuators.
Moreover, high amplitude control signals may weaken the robustness of the control method, and small variations in control parameters may lead to serious performance degradation.
It is, therefore, an object of the present invention to provide a method for controlling an active control system, in which the combination of the energy from the sensors and the energy to the actuators is optimised.
This object is achieved by a method according to the preamble of claim 1, characterised in that the method comprising the step of minimizing a criterion function J defined as a mixture of energy of an observed output error signal vector xcex51(t) and energy of a control error signal vector xcex52(t), defined as:
xcex51(t)=P(qxe2x88x92)y(t)
xcex52(t)=Q(qxe2x88x921)u(t)
with:
P(qxe2x88x921)=an Mxc3x97M dimensional rational weighting matrix of the output sensor signals,
Q(qxe2x88x921)=an Lxc3x97L dimensional rational weighting matrix of the actuator signals, the step of minimising the criterion function J comprising the step of recursively updating the controller coefficients in w(t) proportional to the observed output error signal vector xcex51 and proportional to the control error signal vector xcex52.
Minimising the criterion function J will provide a robust control method, enabling limitation of the drive signal to actuators while maintaining performance of the control method.
In an embodiment of the present method, the output error signal vector xcex51(t) is equal to xcex51(t)=P(qxe2x88x921)y(t|w(t)), in which y(t|w(t)) is a prediction output signal vector, corresponding to the output signal vector y(t) of the sensors (4) at time t in the case that the controller coefficients w(t) have been held constant for a period longer than a response time of the predetermined system. If the controller coefficients are time varying (as may occur during adaptation) y(t|w(t)) may differ significantly from the true sensor output y(t).
This embodiment requires some additional computational effort, but provides a more stable control method behaviour.
In an embodiment of the present method, the contributions to the criterion function J of output error signal vector xcex51(t) and control error signal vector xcex52(t) are tuned by nonnegative entries in diagonal matrices K and xcex9, respectively in the criterion function J, the criterion function being defined as       J    =                  lim                  T          →          ∞                    ⁢                        1                      2            ⁢            T                          ⁢                              ∑                          t              =              0                        T                    ⁢                      xe2x80x83                    ⁢                      E            ⁢                          {                                                                    ϵ                    T                                    ⁡                                      (                    t                    )                                                  ⁢                                  (                                                                                                                                          K                            T                                                    ⁢                          K                                                                                            0                                                                                                            0                                                                                                                          Λ                            T                                                    ⁢                          Λ                                                                                                      )                                ⁢                                  ϵ                  ⁡                                      (                    t                    )                                                              }                                            ,      xe2x80x83    ⁢            with      ⁢              xe2x80x83            ⁢              ϵ        ⁡                  (          t          )                      =                            [                                                    ϵ                1                            ⁡                              (                t                )                                      ⁢                                          ϵ                2                            ⁡                              (                t                )                                              ]                T            .      
In this embodiment it is possible to tune the relative importance of each individual output error xcex51 and of each individual control error xcex52 in the criterion function J.
A further embodiment of the present method implements the tuning of matrices K and xcex9 by a supervisory control layer, adapting the nonnegative entries in matrices K and xcex9 in relation to the transfer function H of the predetermined system and the characteristics of the reference signal vector z(t), the output signal vector y(t) and the control signal vector u(t).
This embodiment allows maintaining the desired control behaviour by varying elements in the matrices K and xcex9. E.g., changes in the transfer matrix H of the predetermined system or the frequency contents of reference signal vector z(t) may necessitate adaptation of the elements in the matrices K and xcex9. The supervisory control layer may be extensively trained beforehand. Although normally the matrices K and xcex9 are tuned off line, the supervisory control layer may adjust the values of the elements in the matrices K and xcex9 yielding time variant weight characteristics of matrices K(t) and xcex9(t).
In a preferred embodiment, the controller coefficients in w(t) are recursively updated according to
w(t+1)=w(t)xe2x88x92xcex3(t)[F1(qxe2x88x921,t)K(t)xcex51(t)+F2(qxe2x88x921,t)xcex9(t)xcex52(t)]
in which F1(qxe2x88x921,t) and F2(qxe2x88x921,t) are time-variant rational matrices of dimensions LNIxc3x97M and LNIxc3x97L, respectively, and xcex3(t) is a positive scalar used to tune the rate of convergence of the control method.
This method allows an adaptation of the scalar xcex3(t) to influence the convergence behaviour of the control method.
In a further embodiment of the present invention, F1(t) and F2(t) have a structure according to
F1(t)=F3xe2x88x921(K(t)xcexa81(t))T;F2(t)=F3xe2x88x921(xcex9(t)xcexa82(t))T; and
xe2x80x83F3=E{xcexa81T(t)KT(t)K(t)xcexa81(t)+xcexa82T(t)xcex9T(t)xcex9(t)xcexa82(t)}
in which xcexa81(t)=PH"PHgr"T(t), and xcexa82(t)=Q"PHgr"T(t).
In this embodiment, the controller will be stable, and have an optimal convergence and tracking speed, by selecting a specific structure for the transfer matrices F1(t) and F2(t), which control the feedback of errors xcex941 and xcex51 to the controller coefficients w(t).
Preferably, the matrix inversion F3xe2x88x921 is calculated off-line, stored in a memory and retrieved when needed, such that the total real-time computational demand is smaller.
Preferably, F1, F2(t), F3(t) and its inverse F3xe2x88x921(t) are tuned simultaneously with the tuning of K and xcex9, as this will maintain the favourable characteristic of convergence rate equalisation and stability of the control method.
Also, in a further embodiment, F3(t) is preferably updated as function of matrices K and xcex9 by using a rank one updating algorithm, e.g. the rank one QR update algorithm as described in G. H. Golub and C. F. van Loon, xe2x80x9cMatrix computationsxe2x80x9d, Johns Hopkins University Press, 1996. This is a computationally efficient way for updating F3(t).
Preferably, the matrix xcex9 is tuned versus matrix K to provide a predetermined balance between performance at the output sensors and required control effort. In general, the bigger the values on matrix xcex9, the higher the robustness of the control method, at the expense of performance at the output sensors, and vice versa.
According to an embodiment of the method, the values of diagonal entries of matrix xcex9 are raised, such that the real parts of the eigenvalues of a matrix A remain greater than zero under changes in the real transfer matrix H, the matrix A being defined as A=E{F1(t)K(t)"PHgr"1(t)+F2(t)xcex9(t)"PHgr"2(t)}
In this embodiment, the chance of an unstable recursion is diminished and the control system remains very robust.
In a further embodiment, the control actuator signals u(t) are limited by setting specific values of diagonal entries of matrix xcex9. This allows a natural convergence of the control method with a certain performance and simultaneously limits drive signals to each of the actuators which require such a restriction.
The supervisory control layer may implement the step of tuning the nonnegative entries in matrix K to provide a higher weight to predetermined elements of the output error signal xcex51(t). This allows a flexible way of taking into account the relative importance of the output signals of the sensors in the predetermined system.
In a further aspect, the present invention relates to an active sound suppression system or an active vibration suppression system comprising at least one actuator, at least one sensor for providing an output signal vector y(t), a controller for providing a control signal vector u(t) to the at least one actuator, a reference signal generator for providing at least one reference signal z(t) to the controller, and an update unit, receiving the output signal vector y(t) and providing a controller coefficient vector w(t) to the controller, in which the update unit and controller are arranged to execute the method according to the present invention.
For the person skilled in the art, it will be clear that the present method can be advantageously implemented in a software program. The software program will then be run on a computer, interfaced with hardware elements of the present system under control, i.e. the actuators and sensors.